Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Secondary Live Problems and Recent Solutions

### Secondary Live Problems

### Flipping Twisty MatricesLive

### A Powerful MatrixLive

### Square PairLive

### Two and Four Dimensional NumbersLive

### Fix Me or Crush MeLive

### Matrix MeaningLive

### Transformations for 10Live

### Secondary Students' Solutions

### Subtraction Surprise

### Non-transitive Dice

### Pair Products

### Pick's Theorem

### Square Remainders

### Divisible Factorisations

### Proper Factors

### Square Difference

### Sissa's Reward

### Square It

### Parallelogram It

### Rhombus It

### Calculating with Cosines

### Trig Identity

### T for Tan

### Loch Ness

### Making Waves

Or search by topic

Each time you visit the NRICH site there will be some activities which are 'live'. This means we are inviting students to send us solutions, and we will publish a selection of them, along with each student's name and their school, a few weeks later. If you'd like to know more about what we're looking for, read this short article.

The last day for sending in solutions to these live problems is Monday 27 November.

Age 14 to 18

Challenge Level

Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

Age 14 to 18

Challenge Level

What happens when you find the powers of this matrix?

Age 14 to 18

Challenge Level

Explore the shape of a square after it is transformed by the action of a matrix.

Age 16 to 18

Challenge Level

Matrices and Complex Numbers combine to enable us to create four dimensional numbers.

Age 16 to 18

Challenge Level

Can you make matrices which will fix one lucky vector and crush another to zero?

Age 16 to 18

Challenge Level

Explore the meaning behind the algebra and geometry of matrices with these 10 individual problems.

Age 16 to 18

Challenge Level

Explore the properties of matrix transformations with these 10 questions.

Take a look at these recently solved problems.

Age 7 to 14

Challenge Level

Try out some calculations. Are you surprised by the results?

Age 11 to 14

Challenge Level

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

Age 14 to 16

Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

Age 14 to 16

Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Age 16 to 18

Challenge Level

What is the remainder if you divide a square number by $8$?

Age 16 to 18

Challenge Level

Can you show that $n^5-n^3$ is always divisible by $24$?

Age 16 to 18

Challenge Level

Can you find the smallest integer which has exactly 426 proper factors?

Age 16 to 18

Challenge Level

Which numbers can you write as a difference of two squares? In how many ways can you write $pq$ as a difference of two squares if $p$ and $q$ are prime?

Age 11 to 14

Challenge Level

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

Age 11 to 16

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Age 11 to 16

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram.

Age 11 to 16

Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus.

Age 14 to 18

Challenge Level

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?

Age 16 to 18

Challenge Level

In this short challenge, can you use angle properties in a circle to figure out some trig identities?

Age 16 to 18

Challenge Level

Can you find a way to prove the trig identities using a diagram?

Age 16 to 18

Challenge Level

Draw graphs of the sine and modulus functions and explain the humps.

Age 16 to 18

Challenge Level

Which is larger cos(sin x) or sin(cos x) ? Does this depend on x ?